The quality of images in magnetic resonance imaging is dependent upon the homogeneity of the respective instrumental components used to generate the image. Much attention has been given to the design and development of magnets having the necessary homogeneity over the imaging volume. Variations in magnetic field homogeneity manifest themselves as image distortions and intensity variation from the true values. Radio frequency (rf) coil inhomogeneity results in non-uniform excitation of the nuclear spins resulting in intensity variations, while deviation from linearity of the gradient field from application of the pulsed field gradients induces image translation and distortions.
More specifically, the quality of a magnetic resonance image is dependent upon the accuracy by which physical position is spatially encoded. As MRI data is now used routinely for stereotaxy, longitudinal studies of atrophy and functional studies, ensuring images have no distortion and inhomogeneity is critical. The principal machine dependant sources of this inhomogeneity previously recognized in the art are eddy currents, gradient non-linearity, B0 and B1 inhomogeneity. See Tanner S F, Finnigan D J, Khoo V S, Mayles P, Dearnaley D P, Leach M O. Radiotherapy planning of the pelvis using distortion corrected MR images: the removal of system distortions. Phys Med Biol. 2000 August; 45(8):2117-32.
As discussed in detail below, the present invention in accordance with certain of its aspects is directed to an analytical approach for calculating and removing the effects of non-linear gradients. Non-linear gradients have been addressed because of the recent interest in short-bore high-speed gradients.
In particular, there has been recent significant interest in the development of gradients having rise times less than 200 μseconds. Although peripheral nerve stimulation is a limiting feature of short rise times, such gradients have found use in high-speed echo planar imaging (EPI) of the heart and diffusion tensor imaging of the brain. To achieve short rise times and to avoid peripheral nerve stimulation, gradient designers have restricted the length of the gradients and limited the number of turns. These limitations, although suitable for the implementation of pulse sequences having the desired speed, have the undesired consequence of increased non-linearity in the gradient fields. The result is distorted images.
More particularly, non-linear pulsed field gradients induce image distortions due to incorrect spatial encoding of the signal. If we assume field gradients are linear, it follows that k-space is sampled linearly and thus a fast Fourier transform (FFT) is suitable for reconstruction. However, any deviation from linearity in the gradients results in non-linear data sampling and subsequent errors in image spatial encoding. A non-linear Fourier transformation would allow this data to be correctly transformed to an image. Unfortunately, non-linear Fourier transformation greatly increases computation time by N/log2N, relative to a FFT, making real-time image generation computationally prohibitive.
As discussed fully below, the present invention in accordance with certain of its aspects addresses this problem and provides a general analytical solution to correct image distortions induced by gradient non-linearity which: (1) is applicable to any gradient configuration, (2) is robust, and (3) importantly, maintains the FFT as the method for image reconstruction.
Mapping and correcting of MRI distortions has been previously considered in the art and attempts have been made to correct the image distortion induced by the non-linearity of the gradients produced by the gradient coils. Two early papers by Schad et al discuss “pincushion” effects seen with 2D phantoms. See Schad L, Lott S, Schmitt F, Sturm V, Lorenz W J. Correction of spatial distortion in MR imaging: a prerequisite for accurate stereotaxy. J Comput Assist Tomogr. 1987 May-June; 11(3):499-505; and Schad L R, Ehricke H H, Wowra B, Layer G, Engenhart R, Kauczor H U, Zabel H J, Brix G, Lorenz W J. Correction of spatial distortion in magnetic resonance angiography for radiosurgical treatment planning of cerebral arteriovenous malformations. Magn Reson Imaging. 1992; 10(4):609-21.
Subsequent schemes include:                (1) using a stereotaxic frame as a reference marker (see Maurer C R Jr, Aboutanos G B, Dawant B M, Gadamsetty S, Margolin R A, Maciunas R J, Fitzpatrick J M. Effect of geometrical distortion correction in MR on image registration accuracy. J Comput Assist Tomogr. 1996 July-August; 20(4):666-79; and Moerland M A, Beersma R, Bhagwandien R, Wijrdeman H K, Bakker C J. Analysis and correction of geometric distortions in 1.5 T magnetic resonance images for use in radiotherapy treatment planning. Phys Med Biol. 1995 October; 40(10):1651-4);        (2) comparing phantom images from CT and MRI (see Fransson A, Andreo P, Potter R. Aspects of MR image distortions in radiotherapy treatment planning. Strahlenther Onkol. 2001 February; 177(2):59-73; and Yu C, Petrovich Z, Apuzzo M L, Luxton G. An image fusion study of the geometric accuracy of magnetic resonance imaging with the Leksell stereotactic localization system. J Appl Clin Med Phys. 2001 Winter; 2(1):42-50); and        (3) imaging specific MRI phantoms that typically consist of an array of tubes filled with a suitable contrast agent (see Bakker C J, Moerland M A, Bhagwandien R, Beersma R. Analysis of machine-dependent and object-induced geometric distortion in 2DFT MR imaging. Magn Reson Imaging. 1992; 10(4):597-608; Mizowaki T, Nagata Y, Okajima K, Murata R, Yamamoto M, Kokubo M, Hiraoka M, Abe M. Development of an MR simulator: experimental verification of geometric distortion and clinical application. Radiology. 1996 June; 199(3):855-60; Woo J H, Kim Y S, Kim S I. The correction of MR images distortion with phantom studies. Stud Health Technol Inform. 1999; 62:388-9.; and Tanner et al., supra).        
A later Mizowaki et al paper (Mizowaki T, Nagata Y, Okajima K, Kokubo M, Negoro Y, Araki N, Hiraoka M. Reproducibility of geometric distortion in magnetic resonance imaging based on phantom studies. Radiother Oncol. 2000 November; 57(2):237-42) alludes to an important problem with phantom studies; after assessing the reproducibility of their own phantom based correction, the authors conclude that such correction may be only applicable in limited situations.
Field mapping is another approach to determining distortion via induced phase shift (see Chang H, Fitzpatrick J M. A technique for accurate magnetic resonance imaging in the presence of field inhomogeneities. IEEE Trans. Med. Imaging, 11: 319-329, 1992; Chen N K, Wyrwicz A M. Optimized distortion correction technique for echo planar imaging. Magn Reson Med. 2001 March; 45(3):525-8; and Cusack R, Brett M, Osswald K. An evaluation of the use of magnetic field maps to undistort echo-planar images. Neuroimage. 2003 January; 18(1):127-42). In particular, the Chang et al. approach relies on the acquisition of two images using different gradient strengths. From the induced phase shift across the difference image a distortion map of the gradient field can be calculated and the images corrected. Other correction schemes have been proposed for particular problems including a post-processing method for correcting distortions induced when using bi-planar gradients (see Liu H, An efficient geometric image distortion correction method for a biplanar planar gradient coil. Magnetic Resonance Materials in Physics, Biology and Medicine, 10: 75-79, 2000). Regardless, these approaches are of limited use in attempting to discern, model or correct distortion due to part of the MRI system in isolation, specifically, the gradients.
In a recent paper (see Langlois S, Desvignes M, Constans J M, Revenu M. MRI geometric distortion: a simple approach to correcting the effects of non-linear gradient fields. J Magn Reson Imaging. 1999 June; 9(6):821-31), a method has been suggested for the correction of both the intensity variations and geometric distortions induced by non-linear gradients based on treating gradient coils as either an opposed Helmoltz pair for the Z-gradient and a Golay arrangement for the transverse gradients. However, this approach treats the non-linear component of the gradient field as a constant for the intensity correction and demonstrates correction of the non-linear induced distortion by correcting a large phantom (a cube of approximately 20 cm length). It is also assumed that for the chosen gradient geometry only second order terms are important. Whilst this approach is useful for gradients with a significant length to diameter ratio (>2), it is of limited use with current high-speed gradients with significant higher order gradient field impurities.
In a recent patent (see Krieg R, Schreck O. U.S. Pat. No. 6,501,273, issued Dec. 31, 2002), it has been suggested that spherical harmonics may be useful in developing a general robust method, but none is given. Another patent application (see Zhu Y, U.S. Patent Application Publication No. US 2002/0093334, dated Jul. 18, 2002) has suggested a method to reconstruct k-space based upon an assumed non-linearity. The method proposed involves approximately 1014 triple integrations and thus is of limited practical value. Indeed, this patent publication highlights one of the primary deficiencies in the art—namely, the failure to realize that any method, which is of practical value, must use the FFT as its basis.
From the foregoing, it can be seen that there exists an established need in the art for a general method for correcting image distortions due to gradient non-linearity. In particular, a need exists for a method that is based on a rigorous approach to the problem allowing clinicians confidence in their image interpretation.
This invention in accordance with certain of its aspects provides such a general method to correct image distortions induced by gradient non-linearity. Significantly, the method is applicable to any gradient configuration.
In addition to the problem of non-linearity, in the course of developing the analytical techniques described below, it was discovered that the field generating devices of a typical MRI system can have (i) substantially displaced symmetry points, i.e., the symmetry points do not share a common center (the non-coincident center problem), and (ii) substantial deviations from ideal geometric alignment, i.e., the individual Cartesian coordinate systems associated with the individual field generating devices, in addition to having displaced centers, can also be rotated relative to each other and/or relative to the overall Cartesian coordinate system of the MRI system (the axes misalignment problem). Such translational and rotational misalignments in and of themselves produce distortions in MR images. Winding and/or design errors for the field generating devices are another source of distortion (the winding error problem). In accordance with others of its aspects, the present invention also addresses the problems associated with these sources of distortion.